Alan Stummer
Research Lab Technologist
Block diagram

"Diff Con 1" Differential Conductance

Warning:  This is a work in progress.  Take everything with a grain of salt!

I am curious who uses what. Are these webpages a waste of time, or are they any help to others?  Are the circuits, software and utilities appearing in other labs?  Please send your comments or suggestions or what you have used (or not) or schematics of your version or pictures or anything!   Email me, or be creative and send a postcard! I want to hear from the vacuum! Links

NOTICE: This webpage and associated files are provided for reference only. This is not a kit site!  It is a collection of my work here at the University of Toronto in the Physics department. If you are considering using any schematics, designs, or anything else from here then be warned that you had better know something of what you are about to do.  No design is guaranteed in any way, including workable schematic, board layout, HDL code, embedded software, user software, component selection, documentation, webpages, or anything.

All that said, if it says here it works then for me it worked. To make the project work may have involved undocumented additions, changes, deletions, tweaks, tunings, alterations, modifications, adjustments, waving of a wand while wearing a pointy black hat, appeals to electron deities and just plain doing whatever it takes to make the project work.


Started 2013 May for Parisa Zareapo in Ken Burch's lab.  This apparatus measures static and dynamic (AKA differential) resistance (or conductance) of junctions with two materials, where one, both or neither may be superconducting.  A sub-Volt DC voltage with a small AF AC excitation is applied to a 4-wire sample in a cryostat.  The AC and DC voltages and currents are measured and sent back to the host (the controlling computer).  The sample is galvanically isolated from the cryostat and any ground or earth.

How It Works

A DAC generates the required static voltage.  An on-board oscillator generates the AC component, the amplitude of which is controlled by a digital pot.  The DC and AC are summed in an opamp with current boosting.  This opamp output is attenuated with selectable low tempco resistors.  Four measurements by four ADCs are made: voltage and current of both the DC and AC components.  AC measurements are phase locked to the AC peak and minimum.  Although the absolute amplitude of the AC voltage and current at its peak and minimum should be the same, both are taken to reduce errors.  Similarly, the AC frequency, which is in the audio range, can be varied to reduce reactive effects of the sample, the cabling and this unit.


Voltage across the sample is with four connections: two current drives and two measurement, also known as Kelvin measurement.  The four connections are BNC.  The BNC shields are connected to the board through 100 Ohms each.  One shield must be connected to an earth ground.  Empirically, experiment with grounds on one or more shields for lowest noise.  This cannot be calculated, it must be tested with trial and error.

Two sets of four BNCs are provided.  They are identical.  While one set may be the sample under test, the other can be a standard resistor used for calibration.  Select the active set with the front panel switch.


Dial Settings

Left - Drive Level               Right - Current Sense
# Normalized Voltage Resistance # DC Resistance AC Resistance
1 out out out 1 1 1
2 1 4.095V 10 2 10 10
3 1 4.095 100 3 100 100
4 0.20325 0.83232 79.7 4 1K 1K
5 0.090909 0.37227 9.0909 5 10K 10K
6 0.020619 0.084433 9.7938 6 100K 90.9K
7 0.099010 0.040545 0.9901 7 1M 500K
8 0.002101 0.008603 0.9979 8 out out
9 out out out 9 out out
10 out out out 10 out out


Gains, Resolution and Measurement s

  • Each measurement returns four values for four parameters: DC voltage, AC voltage, DC current and AC current.
  • Each of these four values is the ADC raw value, from 0 to 65,535 (which is 2^15 - 1).
  • All measurements are bipolar, where midscale (approx 32,768) is zero.  Therefore, positives are greater than that and negatives are less.  The zeros for all four values must be measured before every measurement.
  • Measurements are done at either the peak (90°) or minimum (270°) of the AC cycle.
    • The signed value of each parameter is the measured value minus the measured zero.
    • The signed values of the DC voltages and currents should be the same at either phase.  They can be averaged for better accuracy.
    • The signed values of the AC voltages and currents should be the same magnitude at either phase, but opposite polarities.  The 90° signed values should be positive, the 270° negative.  The absolute values can be averages for better accuracy.
  • The recommended procedure is to take four measurements for every point on the IV curve.
    • At 90° with no DC or AC drive, measure each zero.
    • At 90° with measurement level  DC and AC drive, measure each value,
    • Calculate all four signed values for 90°, as just described above.
    • At 270° with no DC or AC drive, measure each zero.
    • At 270° with measurement level  DC and AC drive, measure each value,
    • Calculate all four signed values for 270°, as just described above.
    • The result is the averages of the 90° and 270° signed values.
Calculated values.  LSB = Least Significant Bit (units)
Measurement Settings per LSB Full Scale Comments
DC Voltage   10.167µV ±333.13mV  
DC Current Depends on current sense setting 11.36µV ±372.3mV Voltage across current sense resistor
AC Voltage Gain X1 62.485µV ±2.048V Do not use, provided for continuity only
Gain X3 20.828µV ±682.50mV Only useful ±200-300mV
Gain X10 6.249µV ±204.75mV  
Gain X30 2.089µV ±68.250mV  
Gain X100 0.6249µV ±20.475mV  
Gain X300 0.2083µV ±6.8250mV  
AC Current
(voltage across
current sense
Gain X1 62.485µV ±2.048V Do not use, provided for continuity only
Gain X3 20.828µV ±682.50mV Only useful ±200-300mV
Gain X10 6.249µV ±204.75mV e.g. Current sense 2 (10^3 or 1K) = 6.25nA/LSB and 205µA FS
Gain X30 2.089µV ±68.250mV  
Gain X100 0.6249µV ±20.475mV  
Gain X300 0.2083µV ±6.8250mV  


Parameter Min Typ Max Conditions and Comments
Drive Source
Load resistance 1 Ohm   1M Ohm  
DC voltage -300mV   +300mV  
DC current -300mA   +300mA Fused at 400mA 
DC resolution   1mV  
AC voltage 0uV   5mV RMS
AC current -   5mA RMS, depending on load
AC frequency 25Hz   1KHz SINAD <1%
Resolution   16   Bits
ENOB   14.5   Measured, estimated

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